3y(y-3)(y-4)=0

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Solution for 3y(y-3)(y-4)=0 equation: 


Simplifying
3y(y + -3)(y + -4) = 0

Reorder the terms:
3y(-3 + y)(y + -4) = 0

Reorder the terms:
3y(-3 + y)(-4 + y) = 0

Multiply (-3 + y) * (-4 + y)
3y(-3(-4 + y) + y(-4 + y)) = 0
3y((-4 * -3 + y * -3) + y(-4 + y)) = 0
3y((12 + -3y) + y(-4 + y)) = 0
3y(12 + -3y + (-4 * y + y * y)) = 0
3y(12 + -3y + (-4y + y2)) = 0

Combine like terms: -3y + -4y = -7y
3y(12 + -7y + y2) = 0
(12 * 3y + -7y * 3y + y2 * 3y) = 0
(36y + -21y2 + 3y3) = 0

Solving
36y + -21y2 + 3y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(12 + -7y + y2) = 0

Factor a trinomial.
3y((3 + -1y)(4 + -1y)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

Move all terms containing y to the left, all other terms to the right.

Simplifying
y = 0

Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3

Subproblem 3
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {0, 3, 4}

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